ECE 431. Experiment #1. Three-Phase ac Measurements. PERFORMED: 26 January 2005 WRITTEN: 28 January Jason Wells

Transcription

1 ECE 41 Experiment #1 Three- ac Measurements PERFORMED: 6 January 005 WRTTEN: 8 January 005 Jason Wells LEADER: Jason Wells RECORDER: Nathaniel Hakes

2 1 ntroduction The primary objectives of the experiment on three-phase ac measurement include becoming familiar with the laboratory equipment as well as reviewing three-phase voltage, current, and complex power relationships studied in previous courses. These objectives were met by investigating a wye-connected resistive load, a delta-connected complex load, and an induction motor operating under no load conditions. This experiment also introduced the one-wattmeter and two-wattmeter methods for measuring reactive and real power, respectively. Discussion and Results.1 and Method Although equipment exists than can directly analyze three-phase real and reactive power, it is often expensive and delicate. As such, it is occasionally desirable to utilize relatively inexpensive single-phase power meters to determine these quantities in the field. This experiment introduced two such methods which are described in [1] on page. n the two-wattmeter method, the total three-phase real power of the load is determined by P = P + 1 P (1) where P 1, P, and, the power factor angle, are given by P1 = Vll cos(0 + ) () P = V l l cos( 0 + ) () = θ θ (4) V Notice that P will be equal to zero if whenever the voltage, current, or cos(-0+ ) is equal to zero. This will occur when the power factor angle,, is equal to either -60 degrees or +10 degrees. Additionally, P 1 will equal P if the power factor angle is equal to zero or 180 degrees (i.e. a purely resistive load). n the one-wattmeter method, the total three-phase reactive power is determined from the observed power by Q = P (5) obs. Balanced Wye-Connected Resistive Load With the one-wattmeter and two-wattmeter methods established, a wye-connected resistive load was tested to observe basic three-phase relationships according to the procedure in [1]. With a wye-connected load, the line-to-line, line, and phase relationships are described ly by V = V = ln Vll (6) = (7) l

3 Raw data observed in the laboratory can be found in Appendix A and is included in Table 1 along with results of several calculations. Total three-phase power and reactive power were calculated using Equations (1) and (5) respectively. Table 1. Experimental Data and Results from the Wye-Connected Resistive Load. - Shift (deg) (P 1 ) (P ) A (A-B) B (B-C) C (C-A) Averages The power factor for a given load can be determined by P P = = S P + Q (8) n the case of the purely resistive load, Q is equal to zero, and the resulting power factor is 1 (unity). Also notice that the P 1 and P are equal for this load as predicted in Section.1. Using the averages in Table 1, Equation (6) can be verified as shown below. V = V = V = 40.7 = V (9) Theoretical ln ll Compared to the observed average phase voltage of 18.8, this is less than a 1 percent error when calculated as V V observed % error = 100% = 0.1% (10) V The line current and the phase current are equal by definition.. Balanced Delta-Connected Complex Load Next, a balanced delta-connected complex load was examined in the laboratory. With a deltaconnected load, the line-to-line, line, and phase relationships are described ly by V = V (11) ll l = (1) Raw data observed in the laboratory can be found in Appendix A and is included in Table along with results of several calculations. Total three-phase power and reactive power were calculated using Equations (1) and (5) respectively.

4 Table. Experimental Data and Results from the Delta-Connected Complex Load. - Shift (deg) (P 1 ) (P ) A (A-B) B (B-C) C (C-A) Averages The power factor for a given load can be determined by P 160 = = =.690 leading S ( ) (1) Since the load is capacitive and reactive power is negative, the power factor is leading. The power factor can be predicted based on the nominal values of R and C in our complex load as shown below where Z is the complex impedance of the load at line frequency. 1 = cos(angle( Z)) = cos(angle( )) = cos( 48.5) = leading (14) 1 + j( π 60) 4uF 15 Comparing this to the power factor as calculated by Equation (1), this is less than a 5% error. (1) % error = 100% =.5% (15) Using the averages in Table, Equation (1) can be verified as shown below. = = 4.96 =.864 A (16) Theoretical l Compared to the observed average phase current of.86 A, this is less than a 1 percent error when calculated as observed % error = 100% = 0.14% (17) The line voltage and the phase voltage are equal by definition. Also notice that the P 1 is greater than P for this load..4 nduction Motor Finally, an induction motor was tested under no load conditions. Again, data was taken regarding its voltage, current, and power magnitudes and is presented for convenience in Table. Total three-phase power and reactive power were calculated using Equations (1) and (5) respectively. factor in the table was calculated using Equation (8) and is lagging since this is an inductive load. Notice that P 1 is less than P for the induction motor at no load. 4

5 Table. Experimental Data and Results from the nduction Motor at No Load. Wattmete r (P 1 ) (P ) - Factor A (A-B) B (B-C) C (C-A) Averages To verify the results of the one-wattmeter method, the total three-phase reactive power observed by this method can be compared against reactive power obtained from voltmeter, ammeter, and power observed in the two-wattmeter method. This alternative reactive power calculation is shown below. ( ll l ) ( ) ( ) ( ) 1 Q = S P = V P + P = (41.)(.66) 175 = 1519 Vars (18) Compared to the one-wattmeter method, this has a percent error of 7.7 %. Q Q calc observed % error = 100% = 7.7% (19) Q calc Conclusions The goals of this laboratory were to become familiar with the laboratory equipment and to review basic three-phase power relationships. n the balanced wye and delta connections, the data indicates that the relationships described in Equations (6-7) and (11-1) are indeed accurate yielding percent errors of less than 1%. Additionally, the data verified that the power factor of a load could be reasonably predicted given the nominal values of the load components. The approximately.5% error in this prediction likely comes from the fact that capacitors have typical tolerances of 5 to 10% on their nominal capacitance. There was a significant percentage error between the three-phase reactive power calculated by the one-wattmeter method compared to using V,, and power from the two-wattmeter method. This error was likely caused by misreading the analog wattmeter display. Ultimately, the data was consistent with predictions and familiarity with the equipment was obtained. References [1] P.W. Sauer, P.T. Krein, P.L. Chapman, ECE 41 Electric Machinery Course Guide and Laboratory nformation, University of llinois at Urbana-Champaign, 005. Appendix (Raw data) 5